490 Curves of Velocity. taneous motion, in direction only, of the two ends P and W of a link, each poiat may be supposed, for the instant, to be travelling in a separate circle, whose radius will be at right angles to the aforesaid motion, and the two radii will,, unless the directions of motion are parallel, meet on one side or other of the line P "W. The meeting point is known as the instantaneous or virtual "centre, and the ratio of the velocities of P and W will be the same as that of the radii Jrom the virtual centre. Of course these may change at every instant, and the centre itself will move along a path known as the centrode. Crank and Connecting Rod (Fig. 452).—In'the position given, W is travelling tangentially, and w D is its virtual radius, while P is moving towards A, and has a radius P D. D then is the virtual centre, and at the instant considered, the movements being along the dotted arcs, pl iv^ vel. P __ D P vel. W ~" DW Taking various other positions, we may obtain a series of virtual centres; and through them draw the centrode E D F, where E and M are the positions of P when W crosses the line K. E. The curve passes out to infinity at F and o, reappearing at L and Q, the direction heing given by the line JP when W is at G and P at H. This means that P and W have then equal velocities. The relative velocities being found for any position, their inversion will give the relation of the forces P and W. Curve of Velocities.—It is often required to construct a curve of velocities for one of the points, when the other mows uniformly. Taking the second diagram in Fig, 452, the triangles w c A. and w P D are similar, so that vel. P _ JDJ> _ A c vel W """* D w "" A w Assuming "W to rnove uniformly, being provided with a fly- wheel, A w will represent crank velocity^ while the projection of P W upon the vertical at c or £ will give AC or &c the piston velocity, In Fig. 453 the value AC is found and transferred to the line A w at A E, and this being done for all positions, the ovals or polar curve may be traced, whose rwttus meter always shews Ps